I know that Afternoon Tea is expensive. I see prices between 60 - 90 Pounds. That works out to $78 - $117 USD.
Do you know if a poor mans afternoon tea is offered in Bath or London? Cost 30 or so Pounds?
Here are recent threads with opinions for Afternoon Tea in London:
https://community.ricksteves.com/travel-forum/england/best-place-to-enjoy-an-afternoon-tea-in-london
https://community.ricksteves.com/travel-forum/england-reviews/in-london-it-s-rules-for-afternoon-tea
In Bath, we enjoyed a reasonably priced afternoon tea at "Hands Georgian Tearoom." http://www.handstearoom.co.uk/. It’s listed in the RS England guidebook.
Have a cream tea as an alternative.
My niece and I thoroughly enjoyed our afternoon tea at Bluebird which is located in the Chelsea area of London. https://www.bluebird-restaurant.co.uk/menus/bar-and-terrace/afternoon-tea/
My daughter and I really enjoyed our afternoon tea at the historic and beautiful Pump Room in Bath, which I think was about 20-25£ per person. It served as our lunch that day and was plenty of food. You will likely need a reservation.
Very pleased with our experience at the Pump Room in Bath. The room itself is just gorgeous and the price is in line with your budget.
We had tea at the Pump Room in Bath too, and it was fine. No need to pay £60+ for a tea.
Afternoon Tea at The Number 16 hotel in South Kensington is nicely done and won’t make a huge dent in your budget.
If you prefer to get out into the suburbs I discovered the Orange Pekoe tea room by chance this past December. Didn’t have afternoon tea but did have the best cream tea and scones. Perfect for a warm up after a morning mudlarking sojourn. It’s a 5-10 minute stroll from the Barnes Bridge Station.
Thanks you for the links and comments. Looks like we can afford tea after all!!
Cheers.